CHAPTER ONE SITE EXPLORATION 2.1 Definition and Purpose
Definition: Site exploration is a term covering field and lab investigations of a site for gathering information on the layers of deposits that underlain a proposed structure for economical and safe design of foundation. It shall always be a prerequisite for foundation design.
Purpose: Site exploration shall be made: To select among alternative sites
To decide on the type and depth of foundation
To estimate the load bearing capacity & probable settlement To select appropriate method of construction
To select and locate construction materials To evaluate the safety of existing structures To determine ground water location
Extent: Site exploration extent depends on: Importance of structure
Complexity of soil conditions Foundation arrangement
Availability of equipment and skill Relative cost of exploration
Information available from performance of existing structures
The least details are required in a highway project, as the soil needs to be explored only up to a depth of 3m or so. More details and deeper explorations are however, required for heavier, multistoried buildings, bridges, dams, etc.
Cost: ranges between 0.1 to 0.5% of the total cost of the project
Information obtained from soil exploration include: general topography and accessibility of the site, location of buried services: power, communication, supply, etc, general geology of the site, previous history and use of the site, any special features (erosion, earth quakes, flooding, seasonal swelling and shrinkage of the soil etc), availability of construction materials, a detailed record of the soil and rock strata including ground water condition, lab and field results of the various strata, results of chemical analysis if any is made etc.
2.1 Planning the Site Exploration (1HLCH-1.doc)
The actual planning of subsurface exploration program includes some or all of the following: 1 Assembly of Available Information
On the specific use of the site, about the site, about the structure- on dimensions, column spacing, type and use, basement or any special requirement etc. Referring building codes is also essential.
2 Reconnaissance Survey:
survey of existing literatures, maps, etc
a close visual inspection by walking over the site
o wrinkling of the surface on a hill side slope and leaning trees soil creep and potential stability problem
2 o Marshy ground with weeds shallow GWT
o Cracks, sags, sticking doors and windows in existing light buildings expansive soils
o Out crops of rocks and profile of existing gullies and cuts, stream patterns, etc indication of the geology of the site
3 Preliminary Ground Investigation:
It is done by making few borings, opening pits and field sounding tests to establish the general stratification. Sampling is mostly limited to acquisition of representative samples. The number of quality samples should be limited to a minimum. Important parameters (like shear strength and compression) are mainly estimated from correlations with the index properties obtained on the representative (disturbed) sample. The information obtained at this stage can be used for preliminary design of the foundation. 4 Detailed Ground Investigation:
Where the preliminary investigation has indicated the feasibility of the project at the site, more detailed site exploration should be under taken. Depending on the results obtained from the preliminary investigation, additional and deeper boreholes may be sunk; more samples extracted (both disturbed & undisturbed); more sounding field tests undertaken to obtain information which shall be sufficient for final design.
2.1 Methods of Site Exploration
The major methods of soil explorations include boring (and sampling), sounding tests, load tests, shear tests, field density tests, geophysical explorations, etc
1. BORING: enables one to extract continuous or discrete samples for visual inspection and testing to determine properties of soils. Methods of boring can be:
a) Test Pits:
Simplest , cheapest method of shallow investigation Provide clear picture of stratification
Weak lenses and pockets can be identified
Block samples can be easily extracted from which undisturbed samples are obtained – called chunk sampling
If GWT is encountered near the ground surface, bore holes are preferred. Pits cannot be dug in silts or sands below the water table or in soft clays because the sides will collapse, endangering the excavation machine & its operator.
Commonly it is uneconomical to go deeper than 5m
It is easier to take good undisturbed soil samples from a trial pit than a bore hole; to carry out in-situ tests (such as SPT & vane shear test)
b) Bore Holes:
Most common for deep investigations Mostly done by power-driven machines Bore hole drilling methods include:
i) Auger boring: boring a hole using augers operated either by hand or machine. Hand operated auger (Figure 1.1)
The hand operated augers may be helical types or post-hole auger.
It can be used for depths up to 3 to 5m. Diameter of holes varies from 5 to 20cm. Generally suitable for all types of soils above water table but suitable only below
water table in clay soils. Soils with boulders & cobbles are difficult to investigate using augers. Also limited use in sandy soils b/c they do not stick to the auger.
Are generally used for making subsoil explorations for high ways, runways, railways etc where the explorations are generally confined to depths of about 5m or so.
Machine operated auger: are suitable in all types of soils and can go to deeper depths. The hollow stem can be used for sampling or conducting SPT test and plugged when not in use. They are capable of penetrating up to 50m.
ii) Wash boring: (Figure 1.2) Is machine operated boring
Involves pushing or driving of casings ahead of boring operation and drilling is facilitated through by means of a chopping bit attached at the bottom of flight of hollow drilling rod. Water is pumped which helps in disintegration and facilitates loosening of the soil. Slurry rises up; screened in to soil solids and water.
The method is rapid except in hard strata and soils with boulders. The machine is light so that it can be easily transported to relatively in accessible areas. It causes not so much disturbance to underlying material.
Undisturbed samples can be extracted easily by pushing thin walled sampler (split spoon sampler). However the effect of water must be taken in to consideration. Disadvantages: - there may be undetected thin layer and high alteration of moisture
content.
iii) Rotary Drilling: (Figure 1.3 (a))
It is generally trailer mounted or lorry mounted.
Bore hole is advanced by power rotated drilling (cutting) bit (2HLCH-1.doc) with
simultaneous application of pressure. The drilling bit is carbide or diamond and is attached to the drilling rods.
Most rapid method in almost all soils. Fluid usually water is used to cool the edges and reduce friction.
Undisturbed sample can be obtained by attaching special sampler usually split spoon sampler.
Disadvantage: not suitable for highly fissured rocks (gravelly soils), as gravels do not break easily, but rotate beneath the bit, expensive
iv) Percussion Drilling: (Figure 1.3 (b))
Involves alternately rising and falling of a heavy chisel-like bit. The drilling activity disintegrates the material below in to the sand silt size. Water is added to loosen soil and chiseler chisels and the loose material (slurry) is scooped out by a bailer. The bailer is generally attached to the boring rod after removing the tool bit at intervals, and then lowered to the hole. It has a non returning valve.
It can be adopted in almost all types of soils, and is particularly useful in very hard soils or soft rocks.
Disadvantage: impossible to detect thin compressible layers, high disturbance of soil, expensive
In all types of drilling used in soft soils that may cave in, casing is used. Drilling mud usually bentonite clay may also be used to stabilize the soil instead of casing.
3.2 Layout, Number and Depth of Bore Holes Layout /Spacing:
While layout of the structure is not yet ready, evenly spaced grid of bore holes is commonly used
Whenever possible bore holes should be located close to proposed foundations For light weight structure like residential houses, it is wise to locate test pits away
from the foundation locations
Approximate spacing of bore holes may be as follows: o Multi storey buildings ---10 m to 50 m
o One storey industrial buildings---20 m to 60 m o Highways ---250 m to 500 m
4 o Dams --- 40 m to 80 m
Figure 1.1: (a) Hand Augers (b) Hollow-stem auger plugged while advancing the auger (c) Hollow-stem auger plug removed and sampler inserted to sample soil below auger
Pulley
Motor
(b) (a)
Figure 1.2: Wash boring Figure 1.3: Drilling types
Number:
It is recommended that a minimum of three bore holes/pits be employed, where the surface is more or less level and the stratification are not so erratic. But if the stratification and topography are far from uniform, it is advisable to use 5 bore holes. Table 1.1 can be used as a guide line.
Table 1.1: Guidelines for preliminary exploration (EBCS 7, 1995) Project
Distance b/n borings (m) Minimum number of borings Horizontal stratification of soil
Uniform Average Erratic
Multi storey building 50 25 10 2 if supplemented with sounding tests otherwise 4
One or two storey building 60 30 15 2
Bridge piers, abutments, towers, etc - 30 7.5 1 to 2 for each foundation
High ways 300 150 30
* Euro Code 7- recommends that the exploration points including sounding from a grid at a spacing of 20 to 40m.
Depth:
Depends on soil condition and magnitude and type of the construction. For highways and air fields a depth of about 2m would suffice. However, if organic soil, muck or compressible soil is encountered, the boring should extend well below the bad soil. Is governed by the depth of influence of the foundation soil contact pressure. Bore
holes should go down to at least the depth below the foundation level at which only 5 to 40% q reaches (q=contact pressure). This translates about 2 to 3 times the foundation width below the foundation level.
It is recommended to make the depth of 1 to 2 bore holes deeper than that of the rest. A minimum of 3m drilling in to a rock formation is recommended especially in area,
where occurrence of boulders is common so as to conform that it is really a rock, and not large boulder.
EBCS 7, 1995 recommends: (3HLCH-1.doc)
- For structures on footings D = 3B > 1.5m - For structures on mat D = 1.5B
- For structures on piles D > D' + 3m , where D' = pile length from surface For preliminary investigation, the depth of exploration may be estimated as:
o
D
3
*
S
0.7 for light steel and narrow concrete buildings oD
6
*
S
0.7 for heavy steel and wide concrete buildingsMotor
driling rod
cutting bit
(a) Rotary Driling (b) Purcussion Driling
casing tool bit chisel Power unit Bailer valve
6 where S = number of stories
3.2 Soil Sampling
Samples of soils are taken from boreholes and trial pits so that the soil can be described and tested. The various types of soil samples to be collected can be divided in to:
1. Non representative Sample: consists of mixture of soil from different soil strata. The size of the soil grains, as well as the mineral constituents, might, thus have changed in such samples. Soil samples obtained from auger cuttings and settlings in sump well of wash boring, can be classified in this category. Such samples may help in determining the depth at which major changes may be occurring in subsurface soil strata. The rock fragments obtained from percussion drilling, soil samples from auger borings and wash boring can hardly be used for the determination of index properties (Like Atterberg limits, grain size distribution, specific gravity, natural moisture content, etc)
2. Representative or Disturbed Sample: is that which contains the same particle size distribution as in the in-situ stratum from which it is collected, though the soil structure may be seriously disturbed. The water content may also have changed. Such disturbed samples can be used for identification of soil types of different strata, for determining Atterberg limits, grain size distribution, specific gravity, natural moisture content, organic and carbonate content, compaction, etc.
3. Undisturbed Sample: is the one that preserves the particle size distribution as well as the soil structure of the in-situ stratum. The moisture content is also tried to be
preserved to its original in-situ value. Such soil samples are required for determination of most important properties of the soil to be used for design. Theses properties include shear strength, consolidation or compressibility and permeability.
Extraction of disturbed samples: this is done by pushing or driving an open ended split spoon sampler in to the soil. The sampler is connected at the bottom to a driving shoe and at the top to a flight of drilling rod by means of coupling. If the natural moisture content is needed, then liner must be employed, which will be waxed at the two ends once the sample is retained. This
is sent to the lab for testing. (4HLCH-1.doc)
Extraction of undisturbed samples: such a sample can be lifted by stopping the boring operation at a certain level and then inserting the appropriate sampler at the bottom of the borehole. When the sampler tube is brought to the surface, some soil is removed from both ends, and molten wax applied in thin layer, to form about 25mm thick seal. Both the ends of the tube are then closed with lids, and transported to the laboratory. Thin-wall samplers with an outer diameter of 5cm (minimum) are used. The common sizes are Do=5cm and Do=7.5cm.
The degree of disturbance of the sample mostly depends on: (4HLCH-1.doc)
Natural cause of removal of the overburden, while collecting samples The impact applied
Rate of penetration of the devices
Dimension of the sampler (cutting edge) and inside wall friction (oil)
If other conditions are kept constant, the degree of disturbance of a sample is roughly indicated by the: a) Area ratio:
100%
*
D
D
D
)
%
(
A
2 i 2 i 2 o r
(5HLCH-1.doc)If Ar < 10%, the sample disturbance can be considered as negligible. However, value up to 25%
is even considered to be good. Thin walled samplers are preferred to thick wall samplers.
b) Inside clearance:
100%
*
D
D
d
)
%
clearance(
Inside
i i i
It should be as low as 1 to 3%. This reduces the frictional resistance between the tube and the sampler. It also allows the slight elastic expansion of the soil sample on entering the tube, and thus assists in sample retention.
c) Out side clearance:
100%
*
d
d
D
)
%
clearance(
side
Out
o o o
It should not be much greater than the inside clearance. It helps in reducing the force required to withdraw the tube.
Spacing of Soil Sampling
It is common practice to take undisturbed samples in a depth range of 0.2m to 0.7m for the top investigation and for the following few meters of investigation, continuous sampling is advisable.
For a fairly good number of boreholes it is usual to extract samples every 1.5m starting from around 0.5m below ground surface or in every layer, which ever is
less. (4HLCH-1.doc)
2. Sounding Tests
2.1 Standard Penetration Test (SPT): (6HLCH-1.doc)
It is really impossible to obtain undisturbed sample from cohesion less soils. Density, strength and compressibility estimates are usually obtained from penetration tests. The objective of SPT is to determine the resistance of the soil to penetration of the standard size of sampler, in order to obtain rough estimate of the properties of the soils in situ. SPT is the most commonly used in situ test in a bore hole. The test is made by making use of a split spoon sampler shown in Figure 1.4 (a). Here a split-spoon sampler is lowered to the bottom of the bore hole by attaching it to the drill rod and then driven by forcing it in to the soil by blows from a hammer (64Kg) falling from a height of 76cm. The sampler is initially driven 15cm below the bottom of the bore hole to exclude the disturbed soil while boring. It is then further driven 30cm in two stages (each 15cm). The number of blows required to penetrate the last 30cm is termed as the SPT
Ri
cutting edge (shoe)
o R ro i r Sampler tube sampler tube
cutting edge (shoe)
i d do i D Do
8
value, or N-value. The test is halted if there is refusal (if 50 blows are required for any 15cm penetration, i.e. N=100, or if 10 successive blows produce no advance). After applying some corrections, this blow count is correlated with important properties of the soil, which can be used for design of foundations. The test is run intermittently with almost all types of boring methods and for any type of soils even if it was developed for cohesion less soils. It has clearly the advantages of enabling one to extract representative samples. It is also economical in terms of cost per unit operation.
Figure 1.4: Standard Penetration Test (SPT) Corrections to Observed SPT
It was regularly observed that the N-value in adjacent boreholes or when using different equipment are not the same. The principal factor is the input energy and its dissipation around the sampler in to the surrounding soil. Energy measurements show that the actual in put energy to the sampler is 70 to 100 % of the theoretical input energy. It is believed that the discrepancies arise from the following factors:
Difference in some features of SPT equipment, drilling rig, hammer and skill of operation Driving hammer configuration and the way hammer load is applied
Whether liner is employed or not
Amount of overburden pressure- the bigger the over burden pressure the more is N value Length of the drill rod- the shorter the rod the more is N value
Bore hole diameter - the smaller the size of the hole the more is N value
Therefore, in order to get approximately the same value for a given soil type at a given depth, it has been suggested to correct the N value as:
N
C
N 1 2 3 470 '
N
Where: N'70 = corrected or modified blow count
CN = adjustment for effective overburden pressure
o N P C ' 76 . 95
P'o= effective overburden pressure at the depth of interest (in KPa)
70 E E E r (i) (70) r (i) r 1
; Er (i) = equipment used for the test (7HLCH-1.doc)Note: Er* N = constant for all equipment [i.e. N70*70=N60*60]
2 = correction for rod length
m L for m L for m L for m L for 4 ; 95 . 0 6 4 ; 85 . 0 10 6 ; 95 . 0 10 ; 0 . 1 2
3 = correction for sample liner
sand loose in liner with clay and sand dense in liner with liner without ; 9 . 0 ; 8 . 0 ; 0 . 1 3
4 = correction for bore hole diameter
mm for mm for mm for 200 ; 15 . 1 150 ; 05 . 1 120 60 ; 0 . 1 4 Correlations of SPT Results
Although the SPT is not considered as refined and completely reliable method of investigation, the N values give useful information with regards to consistency of cohesive soils and relative density of granular soils.
Cohesion less soils
The Japanese Railway Standard proposed
buildings for N bridges and roads for N 27 ' 36 . 0 15 ' 18 70 70
Mayerhof (1959) suggested rD
15
.
0
28
, where Dr = relative density in % Yoshida et al (1988) suggested
0.46 60 12 . 0 ' 25 (%) P NDr o , where P'o =effective pressure in KPa
Skempton (1986): o r
P
D
N
'
288
.
0
32
'
2 70
; where P'o in KPa Terzaghi and Peck also gave the following correlation between SPT value, and Dr.
Table 1.2 : Correlation between N, , and Dr forSands
Condition N'70 degree Dr(%)
Very loose 0-4 <20 0-15 Loose 4-10 28-30 15-35 Medium 10-30 30-36 35-65 Dense 30-50 36-42 65-85
Very dense >50 >42 >85 (8HLCH-1.doc)
10
The common correlations of N-values with unconfined compressive strength of cohesive soils is:
q
u
K
*
N
Where K- is about 12 and qu- in MPa
The following correlations are suggested by Bowels (1995)
Table 1.3 : Correlation between N and qu forClays
Consistency N qu(KPa) gsat(KN/m 3 ) Very soft 0-2 <25 Soft 2-4 25-50 Medium 4-8 50-100 17-20 Stiff 8-15 100-200 Very stiff 15-30 200-400 Hard >30 >400 16-19 19-22
Note: Other dynamic sounding tests can be conducted by using cone instead of split spoon sampler and driving the cone by hammer blows. Depending on the weight of hammer, the drop height and the tip area we have the different types as summarized in Table 1.2.
Table 1.4: Proprties of sounding equipment Type Mass of hammer, m (Kg) Drop height , h (cm) Tip area (cm2) Light penetrometer 10 50 10 Medium penetrometer 30 50 10 Heavy penetrometer 50 50 15 SPT 63.5 76.2 tip open
2.2 Cone Penetration Test (CPT) / Dutch Cone Penetration Test (CPT) It is developed in Dutch and is widely now all over the world. It is a simple test widely used for soft clays and in fine to medium course sands instead of SPT. The test does not have any application in gravels and stiff / hard clays. It is performed by pushing the standard cone (metallic wedge of base area 10cm2 and apex angle of 60o) in to the ground at a rate of 10 to 20 mm/sec for a depth of 13cm and the force is measured and the end resistance of the cone called the cone penetration resistance (point resistance) - qc is computed as the force required to
advance the cone divided by the end area. Then the sleeve is pushed until it touches the top of the wedge followed by pushing both the wedge and the sleeve for 7cm to obtain the combined cone and sleeve resistance, q'c. Then the side resistance (skin friction) q s = q' c- q c. This value
is important for pile design. (9HLCH-1.doc)
Data from CPT can be used to estimate soil profile in conjunction with bore hole driving. Supposing one is required to know the soil profile along axis 1-2-3-4 (Figure 1:6), key boring and sounding tests will be done at points 1 & 4. From the results of the boring and sounding tests one may easily deduce the profile of the soil strata by carrying out sounding tests at points 2 & 3. A number of sounding tests may be made including points 1 & 4 depending on the nature of the stratification
CPT data may also be used to compute bearing capacity of shallow as well as deep foundations.
Correlations of CPT Results
11
Foundation I- Lecture Note Academic Year: 2019/2020 Lancellotta (1983) and Jumilkawiski (1985) suggested the following correlations for the
relative density of granular soil.
v c r q D ' log * 66 98 10
where qc=point resistance (metric tone/m2) and ’v= the effective pressure (metric tone/m2)
12 Figure 1.6: Soil Profile identification
The following table can be used to estimate and the stress strain modulus of compressibility- Es of non cohesive soils
Average point resistance qc (MPa) compactness o Es (MPa)
<5 Very loose (weak) 30 15 - 30
5-10 Loose 32 30 – 50
10-15 Medium dense 35 50 – 80
15-20 Dense 37.5 80 - 100
>20 Very dense 40 100 - 120
Mayne and kempler (1988) suggested for the undrained shear strength (cu)
K v c
N
q
uc
where qc = point resistance (KPa) and v= the total vertical pressure (KPa),
er penetromet cone mechanical for er penetromet cone electric for NK 20 15
For the over consolidation ratio
01 . 1 ' 37 . 0 OCR v v c q
3. Vane shear Test
It is used for the determination of the undrained shear strength (cu) of soft clays (clays
which may be disturbed during the extraction and testing process with cohesions up to 100Kpa). The test is performed at any given depth by first augering to the prescribed depth, cleaning the bottom of the borings, and then carefully pushing the vane instrument (Figure 1.7) in to the stratum to be tested. A torque necessary to shear the cylinder of soil defined by the blades of the vane is applied gradually [by rotating the arm of the apparatus with constant speed of 0.5degree per second] and the peak value noted. The shear strength of the soil can then be estimated by using the formulae derived below.
Figure 1.7: Vane Instrument
The torque is resisted by T1 and T2 (moments about the center)
If both ends of the vane are ‘submerged’ in the soil stratum, and if the maximum shear stress is Cu for all shear surfaces, then
Resisting moment = cylindrical surface resistance + two circular end face resistance Vane dimension (mm) Rod (mm) Drod L = 4r r S Drod 150 37.5 3 16 100 25 1.6 18 S = blade thickness Drod = rod diameter (mm)
T = 2r L (Cu r) + 2[r2 Cu (2/3r)] =2r2Cu (L+2/3r)
L r
r 2π T C 3 2 2u if L 4r (commonly used ratio)
r π 28
3T
Cu 3
If one end of the vane is ‘submerged’ in the soil stratum,
Resisting moment = cylindrical surface resistance + one circular end face resistance T = 2r L (Cu r) + r2 Cu (2/3r) =2r2Cu (L+1/3r)
r L r π 2 T C 3 1 2 u if L 4r r π 26 3T C 3 u (10HLCH-1.doc)The following table gives correlation between consistency and Cu
Consistency BS5930:1981 Terzaghi and Peck: 1967
Very soft <20 <12 Soft 20-40 12-25 Firm 40-75 25-50 Medium 40-75 25-50 Stiff 75-150 50-100 Very stiff >150 100-200 Hard >200
Undrained shear strength Cu(Kpa)
This test is made in every 1 to 2m. Vane shear test is also made in laboratories using small vane instrument.
Field vane shear test overestimates the undrained shear strength. Therefore reduction factor should be used to estimate the design undrained shear strength.
cu, d = cu, The commonly used value of is 0.6. Or one can use curves (Figure 1.8)
to obtain based on the PI value.
Figure 1.8: Bjerrum’s correction factor for vane shear test.
Example 1:
At a depth of 5.8m from the ground level at a site, a shear vane test gave a torque value of 80Nm when fully inserted. The vane is of r=37.5mm.
a) Determine the undrained shear strength of the clay and its consistency
b) If the clay has LL=60%, PL=30%, what would be the undrained shear strength for design Solution: a) Using the formula u 3
r π 28
3T
14 KPa m) 51.65 0375 . 0 ( * 28 10 * 80 * 3 c 3 -3
u Thus the clay has a firm consistency.
c) The design cu will be obtained as cu, d = cu but =f (PI)
PI =60-30=30, For PI=30, = 0.87 (Figure 1.8) cu, d = Pa
4. Plate Load Test
Obviously the most reliable method of obtaining the ultimate bearing capacity and the settlement characteristics at a site is to perform a load test. The test is also used in the design of highways and runways. The probable settlement of the soil for a given loading and at a given depth can also be determined.
Round plate with standard diameter (30cm and 70cm) or square plate of side (0.3m x 0.3m and 60cmx60cm) is loaded in a pit excavated in the ground, at a depth equal to the roughly estimated depth of the foundation for which the bearing capacity is to be estimated. The procedure is:
Excavate a pit to a depth on which the test is to be performed. The test pit should be at least 4B (or 4R) wide as the plate to the depth the foundation is to be placed.
A load is applied on the plate by increments (P=qult, estimated/5), and settlements are recorded
from dial gauges (at least 3 in no.) for each load increment. Then plots of settlement vs. time and settlement vs. applied stress are made.
The test is continued until a total settlement reaches 25mm or until the capacity of the testing apparatus is reached or until the soils fails by shear (plate starts to sink rapidly). Figure 1.9 presents the essential features of the test and typical plots obtained from the plate load test.
When the load vs. settlement curve approaches vertical, one interpolates qult. Sometimes,
however, qult is obtained as that value corresponding to a specified displacement (say, 25mm)
Figure 1.9: Plate Load test Determination of Bearing Capacity from Plate Load Test
Terzaghi and Peck have suggested the following relation between the settlement of the plate Sp
and the settlement of the footing SF:
For sands
2 P F P 0.3 b B 0.3 B b S S p and P P SF B b S for clayswhere: B= width of footing (least dimension) and bp= width (diameter) of plate
The permissible settlement value, such as 25mm, should be substituted for SF in the above
corresponding to the computed settlement SP, is the required value of the ultimate bearing
capacity, qult,P, for the plate. The ultimate bearing capacity of the foundation qult, F is then
determined from qult, P as follows:
For sandy soils ult,P
P F F ult, q B B
q and for clays qult,F qult,P (11HLCH-1.doc)
The coefficient of sub-grade reaction, ks, can also be estimated from:
3
max s KN/m ΔS 0.4σ ΔS Δσ k This parameter is also employed in immediate settlement computation. Limitations of the test
1. Size effects: Since the size of the test plate and the size of the prototype foundation are very different, the results of a plate load test do not directly reflect the bearing capacity of the foundation. The bearing capacity of footings in sands varies with the size of footing; thus, the scale effect gives rather misleading results in this case. However, this effect is not pronounced in cohesive soils as the bearing capacity is essentially independent of the size of footing in such soils.
2. Consolidation settlements in cohesive soils, which may take years, cannot be predicted, as the plate load test is essentially a short-term test. Thus, load tests don’t have much significance in the determination of qall based on settlement criterion w.r.t cohesive soils.
3. The load test results reflect the characteristics of the soil located only within a depth of about 2B of plate. This zone of influence in the case of a prototype footing will be much larger and unless the soil is essentially homogenous for such a depth and more, the results could be terribly misleading. Thus it may be misleading if there is weak soil and ground water with in this influence zone.
5. Indirect Geophysical Methods of Soil Exploration
Geophysical methods correlate speed and condition of wave propagation in a soil media with soil properties. They help us in checking and supplementing the soil test results. They are generally useful in preliminary investigation stage when they can give us ideas about position of the water table, strata boundaries of vastly differing soils, depth of existing bedrocks, etc. The results inferred from such tests must, however, be checked and confirmed from the boreholes, by lifting soil samples, and examining and testing them. Some of these methods are discussed below.
1) Seismic exploration
Such method is based on the simple fact that the seismic waves move through different types of soils at different velocities (4000 to 7000m/s in sound rocks, 500-700m/s in clays, and as low as 30m/s in loose weathered materials) and are also refracted when they cross the boundary between two different types of soils. Here shock waves are induced by producing an explosion at the surface (drop hammer or 3Kg sledge hammer adequate for 20m penetration; deeper with explosive shock source). The waves are then picked up through geophones placed at various points.
This method can help us in plotting the soil profiles, economically, but would fail to detect a layer having velocity lesser than that of the upper layer. Hence a layer of clay laying below a layer of compacted gravel, would go undetected in this method. It is reliable for relatively thick and distinct layers.
16
(12HLCH-1.doc)
Figure 1.10: Seismic Exploration
Interpretation of the test results of seismic exploration should be done with care. Reliable information is only obtained when the soil profile consists of relatively thick and distinct layers. The test results may lead to inaccurate conclusion if the soil profile consists of relatively thin layers. The velocity of longitudinal waves is correlated with the soil type as given in the table below. Shear waves may also be correlated with the soil type.
Soil type Velocity of Longitudinal Waves Vl (m/s)
Non cohesive 200 – 1500
Soils with little cohesion 1000 – 1600
Cohesive soils 1600 – 2000
Rocks 2000 – 6000
2) Electrical Resistivity Method:
This method uses the principle that different soils exhibit different resistivity. As a result four electrodes are inserted in to the ground and current is made to flow. The resistance is then measured. This method requires good contrast in resistivity between the soil layers. If difference between the layers is not substantial, or if the soil is wet and contains a considerable amount of dissolved salt, the reading may be wrong. Clean dense sand above the water table, will therefore have high resistivity, because it will have very small saturation and dissolved salts. Saturated clay of high void ratio will similarly have low resistivity, because there would be a lot of pore water and free ions in it, so as to act as good conductors of electricity, offering very low resistance.
I E 2 x
where: = apparent resistivity in Ohms/m x = electrode spacing
E = potential drop I = circuit current
By increasing electrode spacing, there will be an increase in influence depth. As long as the stratum does not change, remains the same and if changes a new stratum is encountered at a certain depth (approximately at a depth equal to x).
Interpretation of the test results of electrical resistivity method can be made with the help of the following table.
Soil type Resistivity Ohms/m Clay and saturated silt 0 – 1000
Sandy clay 1000 – 2700
Clayey sand and saturated sand 2700 – 5400
sand 5400 – 16400
gravel 16,400 – 50,000
6. ROCK CORE SAMPLING
In rocks, except for very soft or partially decomposed sandstone or lime stone, blow counts are at refusal level (N >100). When rock layer is encountered during driving, rock coring is necessary to check the soundness of the rock. Unconfined compressive strength could also be determined using rock cores. Rock coring is the process in which a sampler consisting of a tube (core barrel) with a cutting bit at its lower end cuts an annular hole in a rock mass, thereby creating a cylinder or core of rock which is recovered in the core barrel. Rock cores are normally obtained by rotary drilling.
Standard rock cores range from about 1 ¼ inches to nearly 6 inches in diameter. The recovery ratio Rr defined as the percentage ratio between the length of the core recovered and the length
of the core drilled on a given run, is related to the quality of rock encountered in boring, but it is also influenced by the drilling technique and the type and size of core barrel used. A better estimate of in situ rock quality is obtained by a modified core recovery ratio as the rock quality designation (RQD) which is expressed as
advance core the of length Total length 100mm core of pices intact of Length RQD
Breaks obviously caused by drilling are ignored. The diameter of the core should preferably not less than 2 1/8 inches. The table below gives the rock quality description, modulus of Elasticity and unconfined compressive strength as related to RQD
RQD (%) Rock Quality E field/ E lab
q
u, field/q
u, lab90-100 Excellent 0.7 – 1.0 0.7 – 1.0 75-90 Good 0.3 – 0.7 0.3 – 0.7
50-75 Fair 0.25 0.25
25-50 Poor 0.2 0.2
0-25 Very Poor 0.15 0.15
If rock is close to the ground surface, it is recommended to drill 2m in sound rock and 3 to 6m in weathered rock.
If rock is encountered at deeper depth, it is recommended to drill 3 to 4m in to the rock, especially below the location of the foundation elements.
18 7. Ground Water
The presence of water table near the foundation affects the load bearing capacity of a foundation. The water table may change seasonally. In many cases establishing the highest and the lowest possible levels of water during the life of the project is necessary. If water is encountered in bore hole during field exploration, the fact should be recorded. In soils with high coefficient of permeability, the level of water in bore hole will stabilize in a bout 24 hrs after completion of the bore hole drilling. The depth of the water table can then be measured using steel tape. In soils with low K-values, this process may take a week. If the seasonal ground water table variation is to be measured, piezometer may be installed in to bore hole and the variation is recorded for longer time. (14HLCH-1.doc)
8. Soil Exploration Report
At the end of all soil exploration programs, after the required information has been collected, a soil exploration report is prepared for the use in the design office. It is a good practice to divide the report in to two:
1. Factual report: include all gathered data
2. Interpretative report: include interpreted data which serve as a basis for design. The report may be presented in the following sections
a) Introduction: which contains information like For whom?
Why?
Method and approach
Terms of reference (TOR) if there is any
b) General description of the site: which should describe
General configuration and surface features like trees, shrubs, buildings, quarries, marshy ground, fill areas, etc
Any useful information derived from past records
Other peculiar observations- wind, earth quakes, slopes, subsidence, etc
c) General geology of the area: which include notes on the geology of the area based on comparison with existing published information and special geologic features like, faults, springs, mine shafts, etc
d) Preparation of the soil profile: This shall describe the various strata in the deposit. It can be best presented by passing an imaginary section through a series of bore holes. The water table location shall be indicated if possible.
e) Laboratory test results : a brief mention of the various tests done is made Due emphasis on unusual tests
For detailed results reference should be made to approximate curves or tables For non standard tests, it is necessary to describe the detailed procedure
followed.
f) Discussion of Results : this is made in relation to implication on design and construction
For example:
In case of shallow foundations, one can recommend depth of foundation, safe bearing capacity, expected settlements a result of superstructure loads provided, advantages and disadvantages of going deeper
In case of pile foundations, one can recommend the bearing stratum, depth of penetration in the bearing stratum, method of installation of the pile, the type of pile to be used (friction/end bearing)
If any detrimental effects on existing structure are possible, it must be well discussed. g) Conclusions: a summary of the main findings of investigation and the
20 CHAPTER TWO
TYPES OF FOUNDATIONS AND THEIR SELECTION 2.1 Types of Foundations
Commonly encountered foundations in practice may be broadly classified into two main categories:
1. shallow foundations (1HLCH-2.doc)
a. Wall or continuous footings (Figure 2.1 (a))
b. Spread or isolated footings and combined footings (Figure 2.1 (b)) c. Mat or raft foundations (Figure 2.1 (c))
2. Deep foundations
a. Pile foundation (Figure 2.1 (d)) b. Piers and caissons (Figure 2.1 (e)) c. Under shallow foundations
22 Figure 2.1………continued
24 Figure 2.1………continued
2.2. Selection of Foundation Types
In selecting the foundation types the following must be considered: a) Function of the structure
b) Loads it must carry c) Subsurface conditions
d) Cost of foundation in comparison with the cost of the superstructure (2HLCH-2.doc)
Having the above points in mind one should apply the following steps in order to arrive at a decision.
1) Obtain at least approximate information concerning the superstructure and the loads to be transmitted to the foundation
2) Determine the subsurface conditions in a general way
3) Consider each of the usual types of foundations in order to judge whether or not a. They could be constructed under existing conditions
b. They are capable of carrying the required load. c. They experience serious differential settlements
4) Undertake a detailed study of the most promising types. Such a study may require additional information on loads and subsurface conditions.
5) Determine the approximate size of footings, piers or caissons or the approximate length and number of piles required.
6) Prepare an estimate for the cost of each promising type of foundation
7) Select the type that represents the most acceptable compromise between performance and cost.
26 CHAPTER THREE
SOME CONSIDERATIONS FOR DESIGN OF SHALOW FOUNDATIONS
3.1 General Requirements (1HLCH-3.doc)
In the design of shallow foundations, the following factors should be considered properly Footing depth and location:
Net and gross bearing capacity
Erosion problems for structures adjacent to flowing water Corrosion protection and sulfate attack
Water table fluctuation
Foundations in sand, silt and clays Foundations on expansive soils Footings should be carried below
- Top soil, organic material, peat or muck
- Unconsolidated material such as abandoned (or closed) garbage dumps and similar filled in areas
- Zones of high volume change due to moisture fluctuations
Use an approximate spacing of footings as m >Zf to avoid interface between ‘old’ and
‘new’ footings
If the ‘new’ footing is in the relative position to the ‘existing’ footing of this figure, interchange the words ‘existing’ and ‘new’.
It is difficult to compute how close one may excavate to existing footings with out having a detrimental effect on the existing footing. If excavation of a new footing is at a depth greater than that of the existing footing there might be a possible settlement of the existing footing because of (a) loss of lateral support of the soil wedge beneath the existing footing (b) loss of overburden pressure-q Nq term of the bearing capacity equation. Thus, it is
recommended to construct a wall (sheet pile wall or other material) to retain the soil in essentially the Ko state out side the excavation.
3.2 SETTLEMENT AND BEARING CAPACITY 3.2.1 SETTLEMENT
1. Definition of settlement
Foundations placed on the soil introduce change in stresses which will compress and deform the underlying soil. The statistical accumulation of the movements in the direction of interest (usually in the vertical direction) is referred to as settlement, S.
A structure may undergo 'uniform settlement' or 'differential settlement'. Uniform settlement or equal settlement under different points of the structure does not cause much harm to the structural stability of the structure. However, differential settlement or different magnitudes of
Existing footing New footing Zf m 45o 2 1
settlement at different points underneath a structure-especially a rigid structure is likely to cause supplementary stress and thereby cause harmful effects such as cracking, permanent and irreparable damage, and ultimate yield and failure of the structure. As such, differential settlement must be guarded against. (2HLCH-3.doc)
2. Data for Settlement analysis: To estimate the settlements we need:
To obtain the soil profile-which gives an idea of the depths of various characteristic zones of soil at the site of the structure, as also the relevant properties of soil such as initial void ratio, grain specific gravity, water content, and the consolidation and compressibility characteristics
To estimate the stresses transmitted to the subsurface strata, using a theory such as Boussinesq's for stress distribution in soil.
3. Total Settlement
The total settlement may be considered to consist of the following contributions: a) Initial settlement or elastic compression.
b) Consolidation settlement or primary compression. c) Secondary settlement or secondary compression.
Initial Settlement or Elastic Compression
This is also referred to as the 'immediate or distortion or contact settlement' and it is usually taken to occur immediately on application of the foundation load (within about 7 days).
Immediate settlement computation (3HLCH-3.doc)
The settlement of the corner of a rectangular base (flexible) of dimensions B' X L' on the surface of an elastic half-space can be computed from an equation from the Theory of Elasticity [e.g., Timoshenko and Goodier (1951)] as follows:
F S s o i I I E v B q S ' 1 2
qo = intensity of contact pressure in units of Es
B' = least lateral dimension of contributing base area in units of S. Es, v = elastic soil parameters
Ii = influence factors, which depend on L'/B', thickness of stratum H, Poisson's ratio v, and
base embedment depth D. The influence factor Is (see Figure 3.1 for identification of terms) can
be computed using equations given by Steinbrenner (1934) as follows:
1 2 1 2
1 2
with and as follows: 1 S v I I I I I v 1 ) 1 )( 1 ( ln ) 1 1 ( ) )( 1 1 ( ln 1 2 2 2 2 2 2 2 2 2 1 N M M N M M N M M N M M M I 1 1
2 tan 2 2 tan in radians
2 1 N M I N M N
B' H N B' L' M where; and 28
i i forcenter and L' L for corner
2 L L' ; corner for B B' and center for 2 B B' I I
IF = influence factor from the Fox (1948b) equations, which suggest that the settlement is
reduced when it is placed at some depth in the ground, depending on Poisson’s ratio and L/B. Figure 3.1 can be used to approximate IF.
Note: if your base is "rigid" you should reduce the Is factor by about 7 percent (that is, Is, rigid =
O.931 Is, flexible)
Figure 3.1: Influence factor IF for footing at a depth D. Use actual footing width and depth
dimension for this D/B ratio.
Determination of Es: Determination of Es-the modulus of elasticity of soil, is not simple
because of the wide variety of factors influencing it. It is usually obtained from a consolidated undrained triaxial test on a representative soil sample, which is consolidated under a cell pressure approximating to the effective overburden pressure at the level from which the soil sample was extracted. The plot of deviator stress versus axial strain is never a straight line. Hence, the value must be determined at the expected value of the deviator stress when the load is applied on the foundation. If the thickness of the layer is large, it may be divided into a number of thinner layers, and the value of Es, determined for each.
Consolidation Settlement or Primary Compression
The phenomenon of consolidation occurs in clays because the initial excess pore water pressures cannot be dissipated immediately owing to the low permeability. The theory of one-dimensional consolidation, advanced by Terzaghi, can be applied to determine the total compression or settlement of a clay layer as well as the time-rate of dissipation of excess pore pressures and hence the time-rate of settlement. The settlement computed by this procedure is known as that due to primary compression since the process of consolidation as being the dissipation of excess pore pressures alone is considered.
The total consolidation settlement, Sc. may be obtained from one of the following
equations: o o 10 o c c σ' Δσ σ' log ) e (1 C H S H Δσ Sc mv
H ) e (1 e S o c
Where, Cc = compression index from the e versus log P plot
eo = in situ void ratio in the stratum where Cc was obtained
H = stratum thickness. If the stratum is very thick (say >6m) it should be subdivided into several sub layers of Hi = 2 to 3m, with each having its own eo
and Cc. Compute the several values of Sci and then sum them to obtain the total
consolidation settlement.
'o = effective overburden pressure at mid-height of H
= average increase in pressure from the foundation loads in layer H and the same units of 'o. The vertical pressure increment at the middle of the layer
has to be obtained by using the theory of stress distribution in soil.
mv = constrained modulus of elasticity determined from consolidation test =1/Es
Time-rate of settlement: Time-rate of settlement is dependent, in addition to other factors, upon the drainage conditions of the clay layer. If the clay layer is sandwiched between sand layers, pore water could be drained from the top as well as from the bottom and it is said to be a case of double drainage. If drainage is possible only from either the top or the bottom, it is said to be a case of single drainage. In the former case, the settlement proceeds much more rapidly than in the latter. The calculations are based upon the equation:
2 v v H C T
Secondary Settlement or Secondary Compression
Settlement due to secondary compression is believed to occur during and mostly after the completion of primary consolidation or complete dissipation of excess pore pressure. It is the continuing readjustment of the soil grains in to a closer (or more dense) state under compressive load. In the case of organic soils and micaceous soils, the secondary compression is comparable to the primary compression; in the case of all other soils, secondary settlement is considered insignificant.
4. Differential Settlement
Non-uniform or differential settlement is settlement in which part of a foundation or two adjoining footings settle differently. If the effect of differential settlement is not taken in to the design of the structure, the structure may crack very badly and the safety of the structure becomes questionable. Basically there are two methods of estimating the allowable differential settlement of a given structure:
1 Analytical methods: expressions derived by introducing simplifying assumptions where stiffness used as a criterion. They may be sometimes misleading and are not used in practice.
2 Empirical methods: previous knowledge or results of field or lab tests are used to determine the settlements.
The magnitudes of the settlements obtained by using the above methods are compared with the permissible amount of settlement.
30
From statistical analysis Skempton and MacDonald concluded that as long as the angular distortion, /l , of a building is less than 1/300, there should be no settlement damage.(Figure 3.2).
1, 2, 3 = differential settlements
= greatest differential settlement Smax = maximum total settlement
l 1, l 2, l 3, = bay width
/l = angular distortion
Figure 3.2: Definition of differential settlement
Having established the permissible limits of differential settlement, various authors have recommended the magnitude of maximum permissible total settlement Smax for practical
purposes. If the maximum total settlement is kept within the permissible limit, the differential settlement, being a function of the total settlement, will also be taken care of.
5. Allowable magnitude of recommended settlement (7HLCH-3.doc)
If the computed settlements are with in the values in the parentheses in the table below, statistically the structure should adequately resist that deformation.
Table: Tolerable settlements of buildings in mm (After Skempton and MacDonald)
Recommended maximum values in parentheses
Criterion Isolated foundation Rafts Angular distortion (cracking) 1/300
Greatest differential settlement
Clays 45 (35)
Sands 32 (25)
Maximum settlement
Clays 75 75-125 (65-100)
Sands 50 50-75 (35-65)
According to EBCS 7 (1995), the permissible total settlement is 50mm and 75mm on sand and clayey soils respectively for isolated footings and correspondingly 75mm and 125mm for rafts.
l1 l2 l3 1 2 3 Ground level Smax Origional foundation level
3.2.2 Bearing Capacity 1. Introduction
To ensure stability, foundations must provide an adequate factor of safety against shear or bearing failure of the underlying soil and the structure must be capable of withstanding the settlements that will result, in particular the differential settlements. Thus the criteria for the determination of the bearing capacity of a foundation are based on the requirements for the stability of the foundation. The design value of the safe bearing capacity would be the smaller of the two values, obtained from the two criteria:
1. Shear failure criterion (10.1HLCH-3.doc)
2. Settlement criterion
The soil’s limiting shear resistance is referred to as the ultimate bearing capacity, qu, of the
soil. For design, one uses an allowable bearing capacity, qall, obtained by dividing the ultimate
bearing capacity by a suitable safety factor (i.e. qall=qu/FS). (10.2HLCH-3.doc)
Some analytical methods of estimating bearing capacity are given below. 2. Terzaghi’s Bearing Capacity Theory
Terzaghi obtained expressions for the ultimate bearing capacity for general shear conditions as:
Husain) S. (Aft er 2 33 45 3t an N t an 2 φ 4 3π e a wit h 1 cos K t an 2 1 N ; cot 1 N N ; 2 / 45 cos 2 N : where N γB 3 . 0 N D γ cN 3 . 1 q : foot ings Circular N γB 4 . 0 N D γ cN 3 . 1 q : foot ings Square N Bγ 2 1 N D γ cN q : foot ings Long 2 pγ 2 p γ q c 2 2 q γ q f c u γ q f c u γ q f c u g a
Table 3.1 below gives the values for the various bearing capacity factors recommended for the above equations.
Table 3.1: Terzaghi’s N-factors
0 2 4 6 8 10 12 14 16 18 20 22 24 Nc 5.7 6.3 6.97 7.73 8.6 9.61 10.76 12.11 13.68 15.52 17.69 20.27 23.36 Nq 1 1.22 1.49 1.81 2.21 2.69 3.29 4.02 4.92 6.04 7.44 9.19 11.4 Ng 0 0.18 0.38 0.62 0.91 1.25 1.7 2.23 2.94 3.87 4.97 6.61 8.58 26 28 30 32 34 36 38 40 42 44 46 48 50 Nc 27.09 31.61 37.16 44.04 52.64 63.53 77.5 95.67 119.67 151.95 196.2 258.29 347.52 Nq 14.21 17.81 22.46 28.52 36.51 47.16 61.55 81.27 108.75 147.74 204.2 287.86 415.16 Ng 11.35 15.15 19.73 27.49 36.96 51.7 73.47 100.39 165.69 248.29 427 742.61 1153.2The
results obtained here are quite within acceptable limits for shallow footings (e.g. Df /B<1)
subjected to only vertical loads. But they are limited to concentrically loaded horizontal footings; they are not suitable for footings that support eccentrically-loaded columns or to tilted footings. Furthermore, they are regarded as somewhat overly conservative.
Terzaghi developed his bearing-capacity equations assuming a general shear failure in a dense soil and a local shear failure for a loose soil. For the local shear failure he proposed reducing the cohesion and as:
tan 3 2 tan ' ' 3 2 ' ' 1 c c
32 3. Meyerhof’s Bearing Capacity Equation
Meyerhof proposed a bearing capacity equation similar to that of Terzaghi but added shape factors, s, depth factors, d, and inclination factors, i.
N 1
tan(1.4 ) N cot 1 N N 2 / 45 tan e N : where d s N Bγ 2 1 d s N D γ d s cN q : Load Inclined q γ q c 2 tan q γ γ γ γ q q q q f c c c c u i i iThe N values are given in Table 3.2 (a) and (b). Table 3.2 (a): Meyerhof’s N- factors
0 2 4 6 8 10 12 14 16 18 20 22 24 Nc 5.1 5.63 6.19 6.81 7.53 8.34 9.28 10.37 11.63 13.1 14.83 16.88 19.32 Nq 1 1.2 1.43 1.72 2.06 2.47 2.97 3.59 4.34 5.26 6.4 7.82 9.6 Ng 0 0.01 0.04 0.11 0.21 0.37 0.6 0.92 1.37 2 2.87 4.07 5.72 26 28 30 32 34 36 38 40 42 44 46 48 50 Nc 22.25 25.8 30.14 35.49 42.16 50.59 61.35 75.32 93.71 118.37 152.1 199.27 266.89 Nq 11.85 14.72 18.4 23.18 29.44 37.75 48.93 64.2 85.38 115.31 158.51 222.31 319.07 Ng 8 11.19 15.67 22.02 31.15 44.43 64.08 93.69 139.32 211.41 328.74 526.47 873.89
Table 3.2 (b): Meyerhof’s factors (s, d, i)
Shape Depth Inclination
Any L B p c 1 0.2K s B D p c 1 0.2 K d 2 0 q c 90 -1 i i For =00 s s 1.0 q g dq dg 1.0 ig 1.0 For >100 L B p q s 1 0.1K s g B D p q d 1 0.1 K d g 2 -1 g i 2 45 tan Kp 2
where = angle of resultant measured from vertical axis
V Q H
When triaxial tr is used for plain strain, adjust tr to obtain ps tr L B 0.1 1.1
Meyerhof suggested that footing dimensions B'=B-2ey and L'= L-2ex be used in determining the
total allowable load eccentrically applied in the x and y directions, respectively (i.e., Qu=qu B'
L'), and in the corresponding terms in the ultimate bearing capacity equations and in the various correction factors for shape and inclination.
4. Hansen’s Bearing Capacity Equation
Hansen proposed the general bearing capacity equation which includes ground factors and base factors to include conditions for a footing on a slope.
u c c c c c c f q q q q q q γ γ γ γ γ γ tan 2 q c q γ q 1 q cN s d b g γ D N s d b g Bγ N s d b g 2where: N e tan 45 / 2 ; N N 1 cot ; N 1.5 N 1 tan [Table 3.3 (a)]
i i i
Expressions for inclination, shape, depth, base, and ground inclination expressions proposed by Hanson are given in Table 3.3 (b).
Table 3.3 (a): Hansen’s N- factors
0 2 4 6 8 10 12 14 16 18 20 22 24 Nc 5.1 5.63 6.19 6.81 7.53 8.34 9.28 10.37 11.63 13.1 14.83 16.88 19.32 Nq 1 1.2 1.43 1.72 2.06 2.47 2.97 3.59 4.34 5.26 6.4 7.82 9.6 Ng 0 0.01 0.05 0.11 0.22 0.39 0.63 0.97 1.43 2.08 2.95 4.13 5.75 26 28 30 32 34 36 38 40 42 44 46 48 50 Nc 22.25 25.8 30.14 35.49 42.16 50.59 61.35 75.32 93.71 118.37 152.1 199.27 266.89 Nq 11.85 14.72 18.4 23.18 29.44 37.75 48.93 64.2 85.38 115.31 158.51 222.31 319.07 Ng 7.94 10.94 15.07 20.79 28.77 40.05 56.18 79.54 113.96 165.58 244.65 368.68 568.59
Table 3.3 (b): Hansen’s factors (s, d, i, b, g) Shape factors ' ' .2 0 sc L B (for =0) ' ' N N 1 s c q c L B (for >) sin L' B' 0 . 1 sq 6 . 0 L' B' 0.4 -1.0 sγ Depth factors k .4 0 dc (for =0) k .4 0 0 . 1 dc (for >0) k 2 q 1 2tan (1 sin ) d 1.0 dγ radians in 1 B D if B D tan 1 B D if B D 1 k k k Inclination factors a f c C A H 1 2 1 2 1 i i (for =0) 1 N 1 q q q c i i i (for >0) 5 2 cot C A V H 5 . 0 1 1 α a f q 1 i i 5 2 cot C A V H 450 7 . 0 1 2 α a f 0 γ 2 i i
Ground factors (base on slope) 0 0 c 147 g (for =0) 0 0 c 147 0 . 1 g (for >) 5 γ q g 1 0.5t g an
Base factors (tilted base)
0 0 c 147 b (for =0) 0 0 c 147 1 b (for >) tan 2 q b e in radians tan 7 . 2 γ b e in radians Notes
Failure can take place either along the long side or along the short side and thus shape , depth and inclination factors shall be calculated in both sides
Use Hi as either HB or HL for inclination factors
< 900; ; D measured vertically.
For L/B < 2 use tr
For L/B>2 use ps=1.5 tr -170 but for tr< 340use tr= ps
= friction angle between base and soil (0. ) Af = B' L' (effective area)
34 5. Vesic’s Bearing Capacity Equation
The Vesic procedure is essentially the same as the method of Hansen with select changes. The Nc and Nq terms are those of Hansen but Ng is slightly different as is given by:
N 1
tan2
Nγ q (also see Table 3.4 (a))
There are also differences in the ii, bi and gi, terms (Table 3.4 (a)).
Table 3.4 (a): Vesic’s Ng - factors
0 5 10 15 20 25 26 28
Ng 0 0.4 1.2 2.6 5.4 10.9 12.5 16.7
30 32 34 36 38 40 45 50
Ng 22.4 30.2 41 56.2 77.9 109.3 271.3 761.3 (10.3HLCH-3.doc)
Table 3.4 (b): Vesic’s factors (s, d, i, b, g) Shape factors L B N N 1.0 s c q c tan L B 0 . 1 sq 6 . 0 L B 0.4 -1.0 sγ Depth factors k .4 0 dc (for =0) k .4 0 0 . 1 dc (for >0) k 2 q 1 2tan (1 sin ) d 1.0 dγ radians in 1 B D if B D tan 1 B D if B D 1 k k k Inclination factors c a f c N C A mH 1 i i (for =0) Where: L/B 1 L/B 2 m m B/L 1 B/L 2 m m L B 1 N 1 q q q c i i i (for >0) m a f q cot C A V H 1 i i 1 m a f γ cot C A V H 1 i i
Ground factors (base on slope) rad in 14 . 5 gc (for =0) tan 14 . 5 1 gc iq iq (for >) 2 γ q g 1.0 t g an
Base factors (tilted base)
c c g b (for =0) tan 14 . 5 2 1 bc (for >)
2 γ q b 1 ηtan b in radians Notes Compute m=mB when Hi=HB (H parallel to B) and m=mL when Hi=HL (H // L). If
you have both HB and HL use
2 L 2
B m
m
m . Note use of B and L, not B',L'.
When =0 and K0, use Ng = -2sin( ) in Ng term
Always iq, ig > 0. For Vesic use B' in the Ng term even when Hi=HL
< 900; ; D measured vertically.
For L/B < 2 use tr
For L/B>2 use ps=1.5 tr -170 but for tr< 340use tr= ps
= friction angle between base and soil (0. ) Af = B' L' (effective area)
